MCS 121, Calculus I, Section 1
(10:30-11:20 MTuThF in OHS 328)

Syllabus: Here is the syllabus.

Office hours for the rest of the semester:

• 11-12 and 3-4:30 Fri, 5/13
• 10:30-12:30 and 1:30-4:30 Mon, 5/16
• 10:30-11:30 and 1:00-3:00 Tue, 5/17

Online resources:

• Webwork is where you do your online homework.
• I use Moodle to post your grades periodically throughout the semester
• The grade calculator allows you to input your current running total from Moodle and see what kind of score you need on the final exam for each kind of letter grade. The calculator is a Google Sheets document, so you need to be logged in to a Google account to access it. It is supposed to work with any Google account, not only your Gustavus account. Click Use Template in the upper right corner to start. You can also download an Excel version of the calculator if Google Sheets does not want to cooperate.
• Here is a list of the topics we have covered. It is updated before each exam.
• Here are my notes to supplement your textbook
  • 1.1. Functions and Their Representations
  • 1.2. A Catalog of Essential Functions
  • 1.3. The Limit of a Function
  • 1.4. Calculating Limits
  • 1.5. Continuity
  • 1.6. Limits Involving Infinity
  • 2.1. Derivatives and Rates of Change
  • 2.2. The Derivative as a Function
  • 2.3. Basic Differentiation Formulas
  • 2.4. The Product and Quotient Rules
  • 2.5. The Chain Rule
  • 3.1. Maximum and Minimum Values
  • 3.2. The Mean Value Theorem
  • 3.3. Derivatives and the Shapes of Graphs
  • 3.5. Optimization Problems
  • 3.7. Antiderivatives
  • 4.1. Areas and Distances
  • 4.2. The Definite Integral
• Desmos is everyone's favorite graphing website.
• Here is an app for visualizing sine, cosine, and tangent on the unit circle.
• This app illustrates the connection between the unit circle and the graphs of sine and cosine.
• Here is another app for visualizing the connection between the unit circle and the graphs of trig functions, including tangent, cotangent, secant, and cosecant.
• This app shows how you can view the graphs of tangent and cotangent as ratios of sine and cosine.
• This app helps to visualize the roles that δ and ε play in the formal definition of limits.
• The following app on secant lines and tangent lines is a good tool to visualize those lines.
• Here is another app on tangent lines.
• Here is yet another app which allows you to see both the tangent line and the corresponding point on the graph of the derivative at the same time.
• Here is an app to visualize the secant line and the tangent line in the Mean Value Theorem.
• The Riemann sums app on Desmos is a good way to visualize how various kinds of Riemann sums approximate the area under a graph.
• Wolfram MathWorld is an interactive math encyclopedia.
• Wolfram Alpha gives you access to many features of Mathematica, an extremely powerful computer algebra program, without paying $$$ and learning Mathematica syntax. It does not only do algebra.

Homework:

Assigned	Due	Read	Exercises
2/3		1.1	No exercises to turn in this week.
2/4	2/11	1.1	Webwork: HW0 (this does not count as part of your grade) Offline: Decide if f: S → T is a function. Carefully justify your answer. S = set of current Gustavus students, T = set of dorms at GAC, f(x) = the dorm x lives in, S = set of people who have ever lived, T = set of people who have ever lived, f(x) = x's father, S = set of people who have ever lived, T = set of people who have ever lived, f(x) = x's youngest brother, S = set of people who have siblings, T = set of people who have ever lived, f(x) = x's oldest sibling, S = set of all triangles, T = set of all line segments, f(x) = x's longest side.
2/11	2/18	1.2	Webwork: HW1 Offline: 1.1.4, 18, 20, 52 Recommended but optional: 1.1.11, 15, 19, 27, 45, 49, 51
2/18	2/25	1.2	Webwork: HW2 Offline: 1.1.42, 62, 66 and 1.2.14 Recommended but optional: 1.1.57, 59, 61, 65 and 1.2.1, 3, 5, 7, 9, 11
2/25	3/4	1.2, 3	Webwork: HW3 Offline: 1.2.4, 26, 38, 44 Recommended but optional: 1.2.13, 19, 27, 31, 35, 37, 43, 55, 57, 61, 63, 65
3/4		1.3	Homework holiday. Review for the upcoming exam.
3/11	3/18	1.3, 4	Webwork: HW4 Offline: 1.3.6, 10, 22, 24 Recommended but optional: 1.3.1, 5, 9, 13, 15, 17, 19, 21, 23, 25
3/18	4/1	1.4 and pp. A15-A19 in Appendix C	Webwork: HW5 Offline: 1.3.32, 40, 44, 46 Recommended but optional: 1.3.26, 27, 29, 33, 35, 37, 39, 41, 43
4/1	4/8	1.4 and pp. A15-A19 in Appendix C, Advice on writing limits	Webwork: HW6 Offline: 1.4.6, 10, 30, 32 Recommended but optional: 1.4.5, 15, 19, 23, 27, 29, 33, 37, 41, 43, 49, 51, 63
4/8		1.4, 5 and pp. A15-A19 in Appendix C	Homework holiday. Review for the upcoming exam.
4/14	4/22	1.5, 6 and 2.1	Webwork: HW7 Offline: 1.4.40, 60, 64 and 1.5.12 Recommended but optional: 1.4.39, 53, 55, 63, 65 and 1.5.5, 7, 13, 15, 17, 25, 29, 31, 33
4/22	4/29	2.1-4	Webwork: HW8 Offline: 1.5.22, 38 and 1.6.34, 52 Recommended but optional: 1.5.21, 23, 27, 37, 39, 47 and 1.6.1, 5, 7, 10, 13, 15, 17, 35
4/29	5/6	2.5 and 3.1-3, 5	Webwork: HW9 Offline: 2.1.14, 2.2.46, 2.3.62, 2.4.57, and 2.5.62 Recommended but optional: 2.1.1, 9, 13, 15, 23, 29, 31, 35, 39, 43 2.2.1, 3, 5, 9, 11, 13, 25, 31, 33, 37, 43, 45, 49 2.3.51, 63, 65, 67, 69 2.4.5, 11, 21, 31, 35, 41, 43, 47, 55 2.5.1, 5, 7, 13, 15, 23, 33, 41, 43, 63, 73, 77
5/6	5/12	3.7 and 4.1, 2	Webwork: HW10 Offline: 3.2.22 and 3.5.30, 32 Recommended but optional: 3.1.5, 11, 13, 29, 43, 49, 57 3.2.5, 9, 15, 21, 23, 33 3.3.5, 7, 15, 29, 49 3.5.9, 13, 17, 27, 29 3.7.7, 9, 29, 39, 43, 55 4.1.5, 7, 11, 15, 17 4.2.5, 7, 15, 21, 39, 47

Exam solutions:

• First midterm exam pdf
• Second midterm exam pdf
• Final exam pdf

Educational links:

• A serious paper on teaching/learning at the university level by Prof. Steven Zucker

Some scholarship opportunities for prospective teachers:

• Knowles Science Teaching Foundation